I didn't know the MK5 had an external fan control module? I thought the controller was built into the larger of the two fans? Where does the module live as I haven't seen one on mine.
With VCDS, have you run an output test on the fans? If you run that (engine off), you will hear and see the fans start at slow speed and then ramp up to full speed. If that passes the test, you can outrule any kind of ground or fan motor issue. The problem then lies with what ever module triggers the fans to come on when the HVAC is set to LO.
You are correct, even after a cold start, both fans should spin when you hit LO on the AC. The fan speed will then vary depending on road speed and ambient temp. The governance over the fans is quite complex unfortunately, and not easy to diagnose. Having said all that, you have actually seen a fan short to ground fault code, which could be intermittent, so it's likely that's the cause of your problem. It could be an internal fault inside the fan itself though, before you start chasing bad grounds and chaffed wires.
Have you checked both fans come on? If only one fan comes on, either the big fat fuse(s) in the engine bay fuse box has blown, or a fan motor has blown (the bigger fan usually goes first).
If you go to VW for new fans, take a mattress with you to fall onto when they give you a price.
Keep at it mate, you're getting there. I think the fan fault code is putting you on the right path.
